If `theta+phi=45^@`, prove that `(cot theta-1) (cot phi-1) =2`.

Prove that : If theta+phi=45^@ , prove that (1+tan theta) (1+tan phi) =2 .

If theta - phi=pi/4 , prove that : (1 + tan theta)(1+tan phi)=2 tan theta .

If theta - phi=pi/4 , prove that : (1 + tan theta)(1-tan phi)=2 .

The base of a triangle is divided into three equal parts. If theta_(1), theta_(2), theta_(3) be the angles subtended by these parts at the vertex, then prove that (cot theta_(1) +cot theta_(2) ) (cot theta_(2)+ cot theta_(3))=4 cosec ^(2) theta _(2)

If 3 tan theta tan phi=1 , then prove that 2 cos (theta+varphi)=cos (theta-varphi) .

Prove that : cot 2A= (cot^2 A-1)/(2 cot A) .

Prove that cot theta cot 2 theta+ cot 2 theta cot 3 theta+ 2= cot theta (cot theta- cot 3 theta) .

If tan (pi cos theta)= cot(pi sin theta) , prove that cos (theta-pi/4)= +- 1/(2 sqrt2) .

If theta+phi= alpha and tan theta=k tan phi , prove that : sin alpha=(k+1)/(k-1) sin (theta-phi) .

If theta and phi are acute angles, sin theta=1/2, cos phi= 1/3 , then the value of (theta + phi) is: